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#pragma once
#include <stdlib.h>
#include <gsl/gsl_rng.h>
#include <gsl/gsl_randist.h>
#include <cmath>
#include "types.h"
template <q_t q, class T>
struct orthogonal_t { bool is_reflection; T *x; };
template <q_t q, class T>
void init(orthogonal_t <q, T> *ptr) {
ptr->is_reflection = false;
ptr->x = (T *)calloc(q * q, sizeof(T));
for (q_t i = 0; i < q; i++) {
ptr->x[q * i + i] = (T)1;
}
}
template <q_t q, class T>
orthogonal_t <q, T> copy (orthogonal_t <q, T> m) {
orthogonal_t <q, T> m_copy;
m_copy.is_reflection = m.is_reflection;
q_t size;
if (m.is_reflection) {
size = q;
} else {
size = q * q;
}
m_copy.x = (T *)calloc(size, sizeof(T));
for (q_t i = 0; i < size; i++) {
m_copy.x[i] = m.x[i];
}
return m_copy;
}
template <q_t q, class T>
void free_spin (orthogonal_t <q, T> m) {
free(m.x);
}
template <q_t q, class T>
vector_t <q, T> act (orthogonal_t <q, T> m, vector_t <q, T> v) {
vector_t <q, T> v_rot;
v_rot.x = (T *)calloc(q, sizeof(T));
if (m.is_reflection) {
double prod = 0;
for (q_t i = 0; i < q; i++) {
prod += v.x[i] * m.x[i];
}
for (q_t i = 0; i < q; i++) {
v_rot.x[i] = v.x[i] - 2 * prod * m.x[i];
}
} else {
for (q_t i = 0; i < q; i++) {
for (q_t j = 0; j < q; j++) {
v_rot.x[i] += m.x[q * i + j] * v.x[j];
}
}
}
return v_rot;
}
template <q_t q, class T>
orthogonal_t <q, T> act (orthogonal_t <q, T> m1, orthogonal_t <q, T> m2) {
orthogonal_t <q, T> m2_rot;
m2_rot.is_reflection = false;
m2_rot.x = (T *)calloc(q * q, sizeof(T));
if (m1.is_reflection) {
for (q_t i = 0; i < q; i++) {
double akOki = 0;
for (q_t k = 0; k < q; k++) {
akOki += m1.x[k] * m2.x[q * k + i];
}
for (q_t j = 0; j < q; j++) {
m2_rot.x[q * j + i] = m2.x[q * j + i] - 2 * akOki * m1.x[j];
}
}
} else {
for (q_t i = 0; i < q; i++) {
for (q_t j = 0; j < q; j++) {
for (q_t k = 0; k < q; k++) {
m2_rot.x[i * q + j] += m1.x[i * q + j] * m2.x[j * q + k];
}
}
}
}
return m2_rot;
}
template <q_t q, class T>
vector_t <q, T> act_inverse (orthogonal_t <q, T> m, vector_t <q, T> v) {
if (m.is_reflection) {
return act(m, v); // reflections are their own inverse
} else {
vector_t <q, T> v_rot;
v_rot.x = (T *)calloc(q, sizeof(T));
for (q_t i = 0; i < q; i++) {
for (q_t j = 0; j < q; j++) {
v_rot.x[i] += m.x[q * j + i] * v.x[j];
}
}
return v_rot;
}
}
template <q_t q, class T>
orthogonal_t <q, T> act_inverse (orthogonal_t <q, T> m1, orthogonal_t <q, T> m2) {
if (m1.is_reflection) {
return act(m1, m2); // reflections are their own inverse
} else {
orthogonal_t <q, T> m2_rot;
m2_rot.x = (T *)calloc(q * q, sizeof(T));
for (q_t i = 0; i < q; i++) {
for (q_t j = 0; j < q; j++) {
for (q_t k = 0; k < q; k++) {
m2_rot.x[i * q + j] += m1.x[j * q + i] * m2.x[j * q + k];
}
}
}
return m2_rot;
}
}
template <q_t q>
void generate_rotation (gsl_rng *r, orthogonal_t <q, double> *ptr) {
ptr->is_reflection = true;
ptr->x = (double *)calloc(q, sizeof(double));
double v2 = 0;
for (q_t i = 0; i < q; i++) {
ptr->x[i] = gsl_ran_ugaussian(r);
v2 += ptr->x[i] * ptr->x[i];
}
double mag_v = sqrt(v2);
for (q_t i = 0; i < q; i++) {
ptr->x[i] /= mag_v;
}
}
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